The geoid height is the separation between the ellipsoid and the geoid with the surface represented as mean sea level.
British Dictionary definitions for ellipsoid
a geometric surface, symmetrical about the three coordinate axes, whose plane sections are ellipses or circles. Standard equation: x²/a² + y²/b² + z²/c² = 1, where ±a, ±b, ±c are the intercepts on the x-, y-, and z- axes
a solid having this shape the earth is an ellipsoid
(ĭ-lĭp'soid') A three-dimensional geometric figure resembling a flattened sphere. Any cross section of an ellipsoid is an ellipse or circle. An ellipsoid is generated by rotating an ellipse around one of its axes.